Intuitively, I’d guess that the most frequent even-digit-count is probably 1, because that’s what it would be for two-digit numbers, as well as numbers in the 100-199 and 300-365 ranges. Only numbers in the 200-299 range would be more likely to have an even-digit-count of 2. (Numbers in the smaller 1-9 range would be more likely to have an even-digit-count of 0.)

Let’s see if this works:

Range

Even-digit-count = 0

= 1

= 2

= 3

1-9

5

4

0

0

10-99

25

45

20

0

100-199

25

50

25

0

200-299

0

25

50

25

300-365

15

33

18

0

Total

70

157

113

25

The intuition is correct: an even-digit-count of 1 is the most likely.